...each, and if the included angle in the first triangle is greater than the included angle in the second, the third side of the first is greater than the third side of the second, and conversely. 1st. Let ACD and PQR be two triangles in which AC is equal to PQ, CD to QR and ACD...

...each, and if the included angle in the first triangle is greater than the included angle in the second, the third side of the first is greater than the third side of /he second, and conversely. 1st. Let ACD and PQR be two triangles in which AC is equal to PQ» CD to...

...sides of the other and the included angle of the first greater than the included angle of the second, the third side of the first is greater than the third side of the second. 3. Show how to draw a tangent to a circle from a point without the circle, and prove your method correct....

...the sum of the squares on the other two sides. 7. Prove that if two triangles have two sides of the one equal respectively to two sides of the other,...first is greater than the third side of the second. 8. Prove that if the middle points of the three sides of a triangle be joined, the triangle formed...

...two sides of another A, but the included Z of the first is greater than the included Z of the second, the third side of the first is greater than the third side of the second). But both these conclusions are contrary to the hypothesis. .-. ZA does not equal ZD, and is not less...

...sides of the other, and the included angles of the first greater than that of the second, prove that the third side of the first is greater than the third side of the second. Also prove the converse of this theorem. 3. Similar triangles (and similar polygons) are to each other...

...equal respectively to two sides of the oiher, but the included angle of the first greater than thc included angle of the second, then the third side of the first will be greater than the third side of the second. ln the triangles ABC and ABE, let AB = AB, BC= BE...

...Proposition XXIV. does it matter in what order the sides are arranged ? PROPOSITION XXV. THEOREM 92. If two triangles have two sides of one equal respectively...A'B'C' to ABC making A'B' coincide with its equal AB. A The angle 'A[ will fall within the angle BAC. Draw AX bisecting the angle CAC and meeting BC in X....

...Proposition XXIV. does it matter in what order the sides are arranged ? PROPOSITION XXV. THEOREM 92. If two triangles have two sides of one equal respectively...GIVEN— two triangles ABC and A'B'C having AB=A'B' and AC— AC, but angle ^4>angle A. To PROVE nC>B'C. Apply A'B'C to ABC making A'B' coincide with its equal...

...two sides and the included angle respectively equal are equal.] If A <A' then would BC<B'C. . § 92 [If two triangles have two sides of one equal respectively...first is greater than the third side of the second ] But both these conclusions contradict the hypothesis. Therefore A>A'. QE 94. CONSTRUCTION. To form...